Trapping time statistics and efficiency of transport of optical excitations in dendrimers

We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and nonradiative decay of the excitations while diffusing across the dendrimer. We derive exact expressions for the Laplace transform of the trapping time distribution and the efficiency of trapping, and analyze those for various realizations of the energy bias, number of dendrimer generations, and relative rates for decay and hopping. We show that the essential parameter that governs the trapping efficiency is the product of the on-site excitation decay rate and the trapping time (mean first passage time) in the absence of decay.     

Theoretical insights into the aggregation-induced emission by hydrogen bonding: a QM/MM study

We investigate the excited-state decay processes for the 3-(2-cyano-2- phenylethenyl-Z)-NH-indole (CPEI) in the solid phase through combined quantum mechanics and molecular mechanics (QM/MM) and vibration correlation formalisms for radiative and nonradiative decay rates, coupled with time-dependent density functional theory (TDDFT). By comparing the isolated CPEI molecule and the molecule-in-cluster, we show that the molecular packing through intermolecular hydrogen-bonding interactions can hinder the excited-state nonradiative decay and thus enhance the fluorescence efficiency in the solid phase. Aggregation effect is shown to block the nonradiative decay process through hindering the low-frequency vibration motions. The fluorescence quantum yields for both isolated molecule and aggregation are predicted to be insensitive to temperature due to the hydrogen-bonding nature, and their values at room temperature are consistent with the experiment.     

Equivalence between the mechanical model and energy-transfer theory for the classical decay rates of molecules near a spherical particle

In the classical modeling of decay rates for molecules interacting with a nontrivial environment, it is well known that two alternate approaches exist which include: (1) a mechanical model treating the system as a damped harmonic oscillator driven by the reflected fields from the environment; and (2) a model based on the radiative and nonradiative energy transfers from the excited molecular system to the environment. While the exact equivalence of the two methods is not trivial and has been explicitly demonstrated only for planar geometry, it has been widely taken for granted and applied to other geometries such as in the interaction of the molecule with a spherical particle. Here we provide a rigorous proof of such equivalence for the molecule-sphere problem via a direct calculation of the decay rates adopting each of the two different approaches.     

Radiative and nonradiative decay rates of a molecule close to a metal particle of complex shape

We present a model to evaluate the radiative and nonradiative lifetimes of electronic excited states of a molecule close to a metal particle of complex shape and, possibly, in the presence of a solvent. The molecule is treated quantum mechanically at Hartree-Fock (HF) or density-functional theory (DFT) level. The metal/solvent is considered as a continuous body, characterized by its frequency dependent local dielectric constant. For simple metal shapes (planar infinite surface and spherical particle) a version of the polarizable continuum model based on the integral equation formalism has been used, while an alternative methodology has been implemented to treat metal particles of arbitrary shape. In both cases, equations have been numerically solved using a boundary element method. Excitation energies and nonradiative decay rates due to the energy transfer from the molecule to the metal are evaluated exploiting the linear response theory (TDHF or TDDFT where TD--time dependent). The radiative decay rate of the whole system (molecule + metal/solvent) is calculated, still using a continuum model, in terms of the response of the surrounding to the molecular transition. The model presented has been applied to the study of the radiative and nonradiative lifetimes of a lissamine molecule in solution (water) and close to gold spherical nanoparticles of different radius. In addition, the influence of the metal shape has been analyzed by performing calculations on a system composed by a coumarin-type molecule close to silver aggregates of complex shape.     

Some aspects of anionic butadiene copolymerization

The relationship between ideal copolymerization behavior and the nature of reactive species in butyllithium (n-BuLi) initiated anionic copolymerization of styrene (St)- butadiene (Bd) in nonpolar solvent has been discussed. The monomer reactivity ratios (m.r.r.) for various reactive species were evaluated by kinetic study and statistical approach (using ¹³C NMR data) in St-Bd anionic copolymerization system with THF as polar additive. The Markovian mechanisms for different propagating reactions in this complex copolymerizing system have been postulated. Furthermore, “pseudo” zero order Markovian mechnism could be sophisticatedly established in the n-BuLi/tertiary amyloxy potassium (t-AmOK)/THF initiated St-Bd copolymerization system, provided that the apparent rate constants of both monomers are equal. Thus, by adjusting the ratio of K/Li and THF/Li, copolymers with composition almost identical to the ratio of initial monomer feed composition at different stages of conversion could be obtained.     

Detailed dynamics of the nonradiative deactivation of adenine: a semiclassical dynamics study

A realistic dynamics simulation study is reported for the ultrafast radiationless deactivation of 9H-adenine. The simulation follows two different excitations induced by two 80 fs (fwhm) laser pulses that are different in energy: one has a photon energy of 5.0 eV, and the other has a photon energy of 4.8 eV. The simulation shows that the excited molecule decays to the electronic ground state from the (1)pipi* state in both excitations but through two different radiationless pathways: in the 5.0 eV excitation, the decay channel involves the out-of-plane vibration of the amino group, whereas in the 4.8 eV excitation, the decay strongly associates with the deformation of the pyrimidine at the C 2 atom. The lifetime of the (1) npi* state determined in the simulation study is 630 fs for the 5.0 eV excitation and 1120 fs for the 4.8 eV excitation. These are consistent with the experimental values of 750 and 1000 fs. We conclude that the experimentally observed difference in the lifetime of the (1) npi* state at various excitations results from the different radiationless deactivation pathways of the excited molecule to the electronic ground state.     

Reevaluating the Solution Photophysics of Tetraphenylethylene at the Origin of their Aggregation-Induced Emission Properties

Although tetraphenylethylene (TPE) and its derivatives have been the most commonly used building blocks in the construction of molecules with aggregation-induced emission (AIE) properties, no absolute consensus exists regarding the mechanisms at the origin of the phenomenon. Restriction of intramolecular rotations (RIR) of peripheral phenyls has historically been a dominant paradigm, which has served as a valuable guideline in the molecular engineering of AIEgens. Yet, an increasing number of recent works have established that photoisomerization or photocyclization may actively participate in the nonradiative dissipation of the excitation energy. In this paper, the first experimental evaluation of the quantum efficiencies of these different processes is reported, and photoisomerization is shown to be by far the dominant photophysical pathway in solution, accounting for virtually all nonradiative decay of the molecule‘s excited state in degassed solution.     

Theoretical insight into the aggregation induced emission phenomena of diphenyldibenzofulvene: a nonadiabatic molecular dynamics study

The diphenyldibenzofulvene (DPDBF) molecule appears in two forms: ring open and ring closed. The former fluoresces weakly in solution, but it becomes strongly emissive in the solid phase, exhibiting an exotic aggregation-induced emission phenomenon. The latter presents a normal aggregation quenching phenomenon, as is expected. We implement nonadiabatic molecular dynamics based on the combination of time-dependent Kohn-Sham (TDKS) and density functional tight binding (DFTB) methods with Tully's fewest switches surface hopping algorithm to investigate the excited state nonradiative decay processes. From the analysis of the nonadiabatic coupling vectors, it is found that the low frequency twisting motion in the ring open DPDBF couples strongly with the electronic excitation and dissipates the energy efficiently. While in the closed form, such motion is blocked by a chemical bond. This leads to the nonradiative decay rate for the open form (1.4 ps) becoming much faster than the closed form (24.5 ps). It is expected that, in the solid state, the low frequency motion of the open form will be hindered and the energy dissipation pathway by nonradiative decay will be slowed, presenting a remarkable aggregation enhanced emission phenomenon.     

Approximate treatment of higher excitations in coupled-cluster theory

The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and implemented methods for total energies is assessed with special regard to quadruple and pentuple excitations. The applicability of our approach is illustrated by benchmark calculations for the butadiene molecule. Our results demonstrate that the proposed algorithm enables us to consider the effect of quadruple excitations for molecular systems consisting of up to 10-12 atoms.     

Photophysical Properties of Au‐CdTe Hybrid Nanostructures of Varying Sizes and Shapes

We design well‐defined metal‐semiconductor nanostructures using thiol‐functionalized CdTe quantum dots (QDs)/quantum rods (QRs) with bovine serum albumin (BSA) protein‐conjugated Au nanoparticles (NPs)/nanorods (NRs) in aqueous solution. The main focus of this article is to address the impacts of size and shape on the photophysical properties, including radiative and nonradiative decay processes and energy transfers, of Au‐CdTe hybrid nanostructures. The red shifting of the plasmonic band and the strong photoluminescence (PL) quenching reveal a strong interaction between plasmons and excitons in these Au‐CdTe hybrid nanostructures. The PL quenching of CdTe QDs varies from 40 to 86 % by changing the size and shape of the Au NPs. The radiative as well as the nonradiative decay rates of the CdTe QDs/QRs are found to be affected in the presence of both Au NPs and NRs. A significant change in the nonradiative decay rate from 4.72×10⁶ to 3.92×10¹⁰ s^?1 is obtained for Au NR‐conjugated CdTe QDs. It is seen that the sizes and shapes of the Au NPs have a pronounced effect on the distance‐dependent energy transfer. Such metal‐semiconductor hybrid nanostructures should have great potentials for nonlinear optical properties, photovoltaic devices, and chemical sensors.     

Nonradiative relaxation in thiophene-S,S-dioxide derivatives: the role of the environment

The intramolecular radiative and nonradiative relaxation processes of three thiophene-S,S-dioxide derivatives with different molecular rigidity are investigated in different solutions and in inert matrix. We show that the fluorescence quantum efficiency and the relaxation dynamics are strongly dependent on the environment viscosity, whereas they are almost independent of the environment polarity. We demonstrate that this strong dependence is due to an environment dependent nonradiative decay rate, whereas no relevant variations of the radiative decay rate are observed. We demonstrate that the dipole coupling with the solvent does not provide an efficient nonradiative decay channel and that the S(n) - S(1) vibrational relaxation is very efficient in all of the molecules and for all of the investigated environments. Moreover first-principles time-dependent density-functional theory calculations in the correct, i.e., excited-state, molecular conformation, suggest that significant contributions of intersystem crossing to the triplet manifold can be excluded. We then conclude that the main nonradiative process determining the fluorescence quantum efficiency of this class of molecules is S(1) - S(0) internal conversion (IC). An explanation for the IC rate dependence in terms of the environment viscosity, molecular rigidity, S(1) - S(0) energy-gap, and molecular volume is presented.     

EXCITON TRANSFER OUT OF OPEN PHOTOSYSTEM II REACTION CENTERS

Abstract A simple photochemical model of photosystem II consisting of antenna chlorophyll and a reaction center was used to examine the phenomenon of exciton detrapping, i.e. the transfer of excitation energy from open reaction centers back to the antenna. η, the ratio of the probability of detrapping when the reaction centers are all open, Ψ_t(o) to the probability when the centers are closed, Ψ_t(x) was used as a variable parameter to examine the various pathways of energy dissipation in a system in which P, the yield of photochemistry, and R, the ratio of the maximum to the minimum yields of fluorescence, were assumed to be known (e.g. R= 4.0 and P= 0.90). It is shown that η must fall within a range of values between 0 and R (1 –P) and that, for given values of R and P, Ψ_t(o) and the ratio of the rate constant for photochemistry at the reaction center, k_p, to the rate constant for energy transfer back to the antenna, k_t, can be determined for any assumed value of η. Even though detrapping occurs at open reaction centers, it is the magnitude of the yield of nonradiative decay at closed reaction centers, Ψ_a(x) which sets the upper limit on η. Equations for the overall yields of fluorescence and nonradiative decay in the antenna chlorophyll and of nonradiative decay at the reaction center chlorophyll, under conditions of both open and closed reaction centers, were derived in conventional probability terms and in terms of R, P and η. As η increases within its range of permissible values, energy dissipation in the antenna decreases and nonradiative decay at the reaction center increases. The determination of a specific value of η or of the ratio k_pk_t would require additional information such as the value of the maximum yield of fluorescence and the ratio of the rate constants for fluorescence and nonradiative decay in the antenna chlorophyll. The characteristics of a system in which there is no nonradiative decay in the reaction center (i.e. k_d= 0), in which case R (1 –P) = 1.0, were also examined. In this case the yield of detrapping has no influence on energy dissipation in the system. Finally, the question of heterogeneity in PSII was considered. It is suggested that Ψ_d(x) may be greater in PSII_β than in PSII_α so that the probability of detrapping could be greater in the PSII_α fraction.     

Femtosecond fluorescence dynamics of rotation-restricted azobenzenophanes: new evidence on the mechanism of trans --> cis photoisomerization of azobenzene

The ultrafast relaxation dynamics of two rotation-restricted (azobenzeno-2S-phane and azobenzeno-4S-phane) and one rotation-free (4,4'-dimethylazobenzene) azobenzene derivatives were investigated using femtosecond fluorescence up-conversion on both S(1)(n,pi) and S(2)(pi,pi) excitations. On S(2) excitation, pulse-limited kinetics with a decay coefficient of approximately 100 fs corresponding to ultrafast S(2) --> S(1) relaxation is found to be common for all molecules under investigation regardless of the molecular structure. This indicates that a direct rotational relaxation on the S(2) surface is unfavorable. On S(1) excitation, we observed biphasic fluorescence decay with a femtosecond component attributed to the decay of the Franck-Condon state prepared by excitation and a picosecond component attributed to the deactivation of the relaxed molecule on the S(1) surface. This picosecond component is slowed by at least a factor of 2 for the rotation-restricted 2S-bridged molecule compared to that of the rotation-free molecule; for the even stronger rotation-restricted azobenzeno-4S-phane, the decrease is by a factor of 10. These differences in deactivation suggest that the relaxed states and probably the trajectories for rotation-free and rotation-restricted molecules are different on the S(1) surface, which should be important for the quantum yield of photoisomerization.     

Nonradiative deactivation of excited hemicyanines studied with submolecular spatial resolution by time-resolved surface second harmonic generation at liquid-liquid interfaces

The excited-state dynamics of aminostilbazolium dyes is known to be dominated by nonradiative deactivation through large-amplitude motion. In order to identify the coordinate(s) responsible for this process, the excited-state lifetimes of two dialkylaminostyryl-methylpyridinium iodides have been measured at liquid-liquid interfaces using time-resolved surface second harmonic generation. We found that the decay time of the excited-states of both compounds was increasing with the viscosity of the apolar phase, consisting of n-alkanes of varying length, but was unaffected by that of the polar phase, made of water/glycerol mixtures. This indicates that the nonradiative deactivation is associated with the twist of the dialkylaniline group, which is located in the apolar part of the molecule.     

Comparison of photophysical properties of the hemicyanine dyes in ionic and nonionic solvents

The fluorescence properties of 4-[4-(dimethylamino)styryl]-1-n-alkylpyridinium bromide (hemicyanine) dissolved in solvents of different polarities and viscosities (methanol, ethylene glycol, tetra-ethylene glycol, glycerol, benzyl alcohol, pyridine, and two ionic liquids, 1-butyl-3-methylimidazolium tetrafluoroborate, [BMIM]BF4, and 1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM]PF6) were investigated. Significant increase in the fluorescence quantum yield and the fluorescence decay lifetime was observed with the increase in the viscosity of the solvent medium. It is because the intramolecular rotational motion of the molecule becomes more difficult in viscous liquid, which leads to a decrease in the nonradiative decay processes. The fluorescence quantum yields for all of the solutions followed a semiempirical law that depends only on the solvent viscosity. The correlation function C(t) was obtained for each solution by joining fluorescence decay curves measured at different wavelengths. From the fitted results of C(t), we observed the distinctive feature unique to the ionic liquids, in which the correlation functions for ionic liquid solutions are fitted to be biphasic, while they are monophasic for other solvents. The fluorescence maximum of hemicyanine dissolved in these ionic liquids red-shifted following the increase in the excitation wavelength.     

Collision-induced nonadiabatic transitions in the second-tier ion-pair states of iodine molecule: experimental and theoretical study of the I2(f0g+) collisions with rare gas atoms

Nonadiabatic transitions induced by collisions with He, Ar, Kr, and Xe atoms in the I(2) molecule excited to the f0(g)(+) second-tier ion-pair state are investigated by means of the optical-optical double resonance spectroscopy. Fluorescence spectra reveal that the transition to the F0(u)(+) state is a dominant nonradiative decay channel for f state in He, Ar, and Kr, whereas the reactive quenching is more efficient for collisions with Xe atom. Total rate constants and vibrational product state distributions for the f-->F electronic energy transfer are determined and analyzed in terms of energy gaps and Franck-Condon factors for the combining vibronic levels at initial vibrational excitations v(f)=8, 10, 14, and 17. Quantum scattering calculations are performed for collisions with He and Ar atoms, implementing a combination of the diatomics-in-molecule and long-range perturbation theories to evaluate diabatic PESs and coupling matrix elements. Calculated rate constants and vibrational product state distributions agree well with the measured ones, especially in case of Ar. Qualitative comparison is made with the previous results for the second-tier f0(g)(+)-->F0(u)(+) transition in collisions with I(2)(X) molecule and the first-tier E0(g)(+)-->D0(u)(+) transition induced by collisions with the rare gas atoms.     

Nonradiative decay processes in benzene

We investigate the behavior of single vibronic level nonradiative decay rates in benzene and benzene-d₆. The effects of excitation in a promoting mode which undergoes frequency and geometry changes in the S₁ relaxation (to T₁ or S₀) are considered in detail. Calculated relative nonradiative decay rates are compared with experimental values and are used to assign triplet state vibrational frequencies to the ν_s, ν₁₀ and ν₁₆ vibrations. This comparison also indicates that none of these modes, nor the modes ν₁ and ν6, are likely to be the dominant promoting modes for the S₁ → T₁ decay. Some simple expressions are given which provide good estimates of the vibronic state dependence of the non-radiative decay rates. In conjuction with experimental decay rate data, these estimates can aid in guiding spectral assignments of vibronic bands. Simple but general theoretical criteria are derived which are useful in determining those vibrations which are poor (or good) accepting modes. Our previous theory is generalized to consider absolute nonradiative decay rates. The results are used to suggest a possible mechanism for the “channel three” decay process observed by Callomon . Although the numerical applications presented here are to benzene electronic relaxation processes, the theoretical developments also apply to and the calcultions illustrate general features of nonradiative decay in the statistical limit.     

The energy gap law for triplet states in Pt-containing conjugated polymers and monomers

The energy gap law established for aromatic hydrocarbons and rare earth ions relates the nonradiative decay rate to the energy gap of a transition through a multiphonon emission process. We show that this energy gap law can be applied to the phosphoresce of a series of conjugated polymers and monomers for which the radiative decay rate has been enhanced through incorporation of a heavy metal. We find that the nonradiative decay rate from the triplet state T(1) increases exponentially with decreasing T(1)-S(0) gap for the polymers and monomers at 300 and 20 K. Comparison of the nonradiative decay of polymers with that of their corresponding monomers highlights the role of electron-lattice coupling.     

Quantum chemistry study on internal conversion of diphenyldibenzofulvene in solid phase

We investigate the nonradiative decay process of diphenyldibenzofulvene (DPDBF) in solid phase by using the quantum chemistry methods. To carry out the nonradiative rate constant calculation, we construct a solid phase model based on the ONIOM method. The geometry of the DPDBF molecule is optimized for the ground state by DFT and the first excited state by TD-DFT, and the corresponding vibrational frequencies and normal coordinates are computed. Under displaced-distorted harmonic oscillator potential approximation, Huang-Rhys factors are obtained. Vibronic coupling constants are calculated as a function of the normal mode based on Domcke's scheme. We find that vibronic coupling constants of 12 modes with large reorganization energies are of similar order, and if this result is still valid for other modes, the internal conversion rate would be determined by high frequency modes because they have a significant nuclear factor that is related to Franck-Condon overlap intergrals. We also find that geometrical changes are suppressed due to the stacking effect, which yields small Huang-Rhys values in the solid phase.     

How the central torsion angle affects the rates of nonradiative decay in some geometrically restricted p-quaterphenyls

A small series of p-quaterphenyl derivatives has been prepared in which the dihedral angle (phi) for the two central rings is constrained by dialkoxy spacers of varying length. The photophysical properties of these compounds remain comparable, but there is a clear correlation between the rate constants for nonradiative decay of both singlet and triplet excited states and phi in fluid solution. The rates tend toward a minimum as phi approaches 90 degrees . These effects are attributed to the general phenomenon of extended delocalization and can be traced to a combination of changes in the Huang-Rhys factor and the electron-vibrational coupling matrix element, both relating to displacement of the relevant potential energy surfaces and to the medium-frequency vibronic mode coupled to decay. The latter effect arises because of different levels of conjugation in the ground-state molecule. Such findings might have important implications for the design of improved light-emitting diodes. A similar angle dependence is noted for the yield of the pi-radical cation formed on photoionization in a polar solvent, but here, the effect is due to variations in the respective energy gaps between the relevant excited states.